Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs
Federal Reserve Board, Washington, D.C.
An Inflation Goal with Multiple Reference Measures
William Whitesell 2005-62
NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.
An Inflation Goal with Multiple Reference Measures
William Whitesell*
December, 2005
Abstract
Most inflation-targeting central banks express their inflation objective in terms of a range
for a single official inflation measure but generally have not clarified the meaning of the
ranges and their implications for policy responses. In formulating policy, all central
banks monitor multiple inflation indicators. This paper suggests an alternative approach
to communicating an inflation goal: announcing point-values, rather than ranges, for a
few key reference measures of inflation that are used in making policy. After reviewing
and extending relevant theoretical and empirical studies, the paper argues that the
alternative approach could more accurately reflect the concerns of policymakers and
provide a better accountability structure for monetary policy performance.
Keywords: inflation targeting, monetary policy regime
JEL classifications: E52, E58, E42
* Board of Governors of the Federal Reserve System ([email protected], 202-452-
2967). I have appreciated the comments of D. Cohen, D. Henderson, J. Kim, B.
Madigan, A. Orphanides, S. Struckmeyer, E. Swanson and other participants at a Board
staff seminar. The views expressed are those of the author and not necessarily those of
the Board of Governors of the Federal Reserve System or others of its staff.
An Inflation Goal with Multiple Reference Measures
I. Introduction
Central banks have adopted inflation goals or more complete inflation targeting
frameworks in order to improve the performance of monetary policy. Improvements are
expected because of better behaved inflation expectations arising from the greater
transparency and credibility of the regime and because of the disciplining of monetary policy
through an enhanced accountability framework.
Central banks with explicit inflation goals have almost universally selected unique
official price measures to represent their objective. However, no central bank would be
satisfied by looking at only one price index when formulating monetary policy. Because
inflation measures differ in methodology, sector coverage, inherent biases, and idiosyncratic
noise, examination of a variety of these indicators has been needed to gain insight into the
underlying inflation process. Why then do central banks generally set aside this richness of
analysis and choose to represent an inflation goal in terms of a single reference measure?
Evidently, they view the simplicity of a unique measure as essential to facilitate
communication with the public and thus to achieve the credibility and accountability
advantages of an inflation-targeting framework.
But central banks and observers recognize that inflation accountability can in some
circumstances be oversimplified or misplaced. One example would be an "inflation nutter's"
excessive focus on inflation control to the exclusion of other important policy objectives,
such as output, employment, and financial stability. Another would be rigid adherence to an
announced point-goal at a time when transitory special factors are distorting the inflation
signal in the chosen measure. Such considerations have induced many central banks to allow
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some wiggle room in accountability discipline by announcing inflation ranges rather than
point-goals and, in some cases, by articulating "escape clauses," or reasons to ignore a miss
of their inflation range.
This paper considers whether the above typical structure of an inflation-goal regime
will prove to be best practice. It assesses whether selection of a single official inflation
measure and use of a range, with occasional escape clauses, is the best accountability
framework for disciplining a central bank and for fostering transparency and credibility
objectives. While a unique official inflation measure may ease communication challenges at
the time of implementation of an inflation goal, the long-run transparency and credibility
benefits of such a framework are less obvious. The analysis is relevant not only for inflation-
targeters, but also for central banks that choose to announce a long-run inflation goal without
the other trappings of an inflation-targeting framework, as advocated for the United States by
Bernanke (2004), among others.
After summarizing key aspects of existing inflation-goal regimes, the paper
investigates the role of inflation ranges in monetary policy frameworks. It then reviews
theoretical research on an accountability standard for central banks and on optimal inflation
indexes. It develops a version of the Mankiw/Reis (2003) model in order to depict how
measurement uncertainties could affect the specification of an optimal price measure.
Empirical evaluations are conducted on whether the choice of an inflation index really
matters and, using factor analysis, whether a unique "underlying inflation process" can be
said to exist. The paper then assesses the implications for central bank accountability of a
range for a single indicator versus point-values for multiple reference measures. A summary
concludes.
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II. Characteristics of Inflation-Goal Regimes
Over the last decade and a half, the practice of announcing specific targets for
monetary policy has become more widespread among central banks. For instance, in a
survey of 91 central banks around the world, Sterne (1999) reported that 87 had an explicit
announced policy target of some kind in 1998 versus only 50 in 1990. The survey also found
that more than half of the central banks had explicit inflation objectives, although in most
cases these goals were combined with target values for other economic indicators as well,
such as money growth or the exchange rate.
Currently, 21 central banks are generally classified as inflation targeters (see Table 1),
based on their priority commitment to an inflation goal and their use of inflation forecasts as
intermediate targets for policy (see IMF, 2005). All but one of these inflation-targeting
central banks use a unique official price measure and all but three employ an inflation range
rather than a point-goal by itself.1 Most of the central banks with ranges emphasize the
center of the range as their point-goal. Ten of the 18 central banks with ranges have
described the ranges as reflecting limits on their ability to control inflation. Nine use the
boundaries of the range as a trigger for a formal communication by the central bank
regarding the behavior of inflation, suggesting a key accountability role. Three central banks
have described their ranges as zones of indifference regarding inflation outcomes.
1 These include a few cases of point-goals associated with "ranges" that are loosely defined or that have "soft edges," such as the Bank of England, which now faces only a reporting requirement if it misses its point inflation target by 1 percentage point or more.
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Table 1: Inflation-Targeting Countries
Country
Target Specification*
Rationales for range (Table 2)
Australia 2-3%, CPI 3, 5
Brazil 3¾ ± 2½%, CPI 10
Canada 1-3%, CPI, 6-8 quarter horizon, also emphasize CPIx
4, 10
Chile 2-4%, CPI, 8 quarter horizon, also emphasize CPIx
4
Colombia 3%, CPI n.a.
Czech Republic 1-3% CPIx, 2-4% CPI 4
Hungary 3½±1% 4
Iceland 2½±1% 10
Israel 1-3%, CPI 10
Korea 2½-3½%, CPIx, medium term horizon 4, 9
Mexico 3±1%, CPI 4
New Zealand 1-3%, CPI, medium term horizon 3, 4, 10
Norway 2.5%, CPIx n.a.
Peru 2½±1%, CPI, Dec.–Dec. 4
Philippines 2½±1%, CPI 10
Poland 2½±1%, CPI 4
South Africa 3-6%, CPIx 3, 4
Sweden 1-3%, CPI, 4-8 quarter horizon 10
Switzerland Less than 2%, CPI, 3 year horizon n.a.
Thailand 0-3½%, CPIx 10
United Kingdom 2±1%, HICP 10
* Sources: Truman (2003), Ayales (2002), and central bank websites. Notes: CPIx implies the deletion of some component(s) from headline consumer prices, such as energy, food, indirect taxes, or mortgage interest in different cases. HICP is the harmonized index of consumer prices.
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As noted in Table 2 and discussed further below, a variety of other interpretations of
an inflation range are possible but have not generally been embraced by central banks. The
alternative rationales imply differences in the appropriate width of an inflation range, in the
variation in that width over time, and in associated monetary policy reaction functions.
However, despite the absence of supportive quantitative analyses, most central banks with
ranges have settled on a fixed range width of 2 percentage points.
As regards inflation indicators, most central banks with explicit inflation goals use
headline consumer prices as a reference measure. This can create problems when transitory
factors make it inappropriate for a central bank to respond to movements in the official
measure. At such times, a central bank may put a substantial weight on core inflation
indicators, which exclude volatile energy and food components, in formulating policy.
Inflation reports generally include discussions of a variety of price indexes, often as a way of
explaining why the deviation of headline inflation from the target is being tolerated and the
extent to which other indicators may be giving a more policy-relevant inflation signal.
For example, the Bank of Canada officially targets headline CPI inflation, but at
times has placed more emphasis on unofficial "operational" targets for measures of core
inflation. It has devoted considerable effort to refining such core measures (Knight et al,
2002).2 The Bank of England's official target, until December 2001, was the retail price
2 The Bank of Canada cut interest rates in early 2001 to address slowing economic growth despite the fact that headline CPI inflation was around the top of the target range. It argued that headline inflation was only temporarily high while pointing out that core inflation was near the midpoint of the range (Knight et al, 2002). The core inflation measure excluded energy, food, and indirect taxes until May 2001 when it was redefined to exclude fruit, vegetables, gasoline, fuel oil, natural gas, intercity transportation, tobacco, mortgage-interest, and indirect taxes.
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Table 2
RATIONALES FOR A RANGE
MIDPOINT EMPHASIS
IMPLIED RANGE WIDTH
Diffuse Goal:
1. Uncertainty about numerical point-goal. In some dynamic specifications
Time- varying
2. Facilitate compromise among policymakers with differing views of appropriate inflation goals.
No Time- varying
3. Flat social welfare function. In some dynamic specifications
Narrow, fixed
Expected Volatility in Inflation:
4. Indicate limits on predictability and control of inflation.
Yes Wide, varying
5. Indicate normal cyclical variation in inflation. Yes Narrow, fixed
6. Indicate an optimal trade-off between inflation stability and output/employment stability.
Yes Wide, fixed
Policy Reaction Function:
7. Outside range only, respond to inflation. No Narrow
8. Outside range, nonlinear response to inflation. Yes Narrow
9. Inside range only, respond to real economy. Yes Wide
Accountability Device:
10. Outside range only, explanations required or penalties imposed.
No*
* While not inherent in this rationale, a midpoint emphasis could nevertheless be
communicated by other means, as is currently the case at the Bank of England.
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index excluding mortgage payments.3 However, as noted by Bowen (1995), "in the Bank,
RPIY [retail price index excluding mortgage payments and indirect and local taxes] is
preferred as a measure of underlying inflation." Also, the Reserve Bank of New Zealand
officially targets the CPI excluding interest costs, but has operational targets for a measure of
underlying inflation that adjusts for indirect taxes as well as terms of trade and other shocks
(Sherwin, 2000). The Riksbank has an official inflation target based on the headline CPI, but
regularly discusses and forecasts several other inflation measures in its quarterly inflation
reports because "various measures of 'core' or 'underlying' inflation ... have at times been
more decisive for monetary policy than CPI forecasts [and] ... the idea that a certain price
index would invariably yield an unambiguous signal about the optimal policy seems ill-
founded" (Heikensten and Vredin, 2002).
III. Uses of Inflation Ranges
A variety of possible competing or overlapping interpretations of inflation ranges are
indicated in Table 2 and grouped for discussion purposes into four categories: a diffuse goal,
expected inflation volatility, a policy response structure, and/or an accountability device.
A range may indicate a diffuse goal owing to uncertainty about the optimal point-
value, compromises among policy makers, or a flat social welfare function. The
uncertainties could be related to the measurement of inflation or to the optimal cushion
above true price stability. For instance, the optimal cushion would vary over time owing to
evolution in the inherent stability of the economy or in the pace of structural productivity
3 It was then changed to the geometric-means-based Harmonized Index of Consumer Prices (HICP), similar to that used by the ECB.
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growth,4 and a range would obviate the necessity of frequent associated adjustments in the
point-goal. The compromise rationale could arise if members of a policy committee could
not agree on a point-goal but could agree on a range encompassing their point-goal
preferences (Santomero, 2004). Along these lines, Tetlow (2000) models an implicit point-
target that drifts in a random walk owing to evolving compromises among policymakers. At
the boundaries of the range, policymakers agree on the need to take action to bring inflation
back in line. Orphanides and Wieland (2000) model a range as reflecting a flat single-period
welfare function. They point out, however, that preferences based on discounted future
welfare would not be indifferent when shocks are persistent, because approaching the
boundaries would then increase the chance of breaching the range in a subsequent period.
Except for such dynamic specifications with persistent shocks, these diffuse-goal rationales
would tend to be associated with ranges as indifference zones and no emphasis on the
midpoint. Ranges of that type have been criticized for failing to provide enough guidance for
the long-run inflation expectations of the public (Bernanke et al, 1999, Faust and Henderson,
2004, Gavin, 2004).
Ranges more typically have been used to signal expected volatility in inflation
outcomes around a midpoint-goal. In these cases, a range could indicate a confidence
interval for inflation control, movements in inflation over the business cycle that the central
bank will allow, or an optimal trade-off with output or employment volatility.
4 Faster trend productivity growth would diminish the need for an inflation cushion to facilitate labor market adjustments in the presence of downward wage rigidity because declining industries could then more easily shrink with slower but still positive wage growth. It would also imply a higher equilibrium real interest rate and thereby reduce the need for an inflation cushion to cope with the risk that the central bank would hit the zero lower bound on nominal interest rates when trying to stimulate the economy.
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The appropriate width of an inflation range in these cases would depend importantly
on the type of volatility that it is intended to signal. The control and trade-off rationales
would likely imply wider ranges than cyclical drift, and the control rationale would probably
be more time-varying. Numerous authors have commented that a typical range width of 2
percentage points is too narrow to signal the limits of inflation control unless inflation
stability improves dramatically (e.g., Debelle and Stevens, 1995, and Haldane and Salmane,
1995). Cyclical movements in inflation have also been more pronounced in the past than
envisioned in this rationale for a range. Estimates of range widths needed in optimal trade-
offs of stabilization goals (Taylor, 1979, Erceg, 2002, Faust and Henderson, 2004) have
differed widely.5
An alternative to using an inflation range to indicate expected inflation volatility is
the "fan chart," or confidence interval that expands with forecast horizon, commonly used in
inflation reports. Fan charts have an advantage over ranges in this role because they allow
for time-varying uncertainty and can be accompanied by situation-specific simulations and
explanations.
A third category of rationales for inflation ranges is as an indicator of the monetary
policy reaction function. For instance, if a range signified an indifference zone, policy
might be expected to respond to inflation only when the range was breached, or perhaps shift
nonlinearly to a stronger response to inflation at that time. Orphanides and Wieland (2000)
5 Reifschneider et al (1999) estimated inflation/output volatility trade-offs for a variety of Taylor-type policy rules using the FRB/US model and found that, on the policy frontier, pushing the standard deviation of four-quarter PCE inflation below 1½ percentage point resulted in the standard deviation of the output gap rising notably above 2 percentage points. Using the same model, Williams (2003) found a slightly better trade-off using a three-year average measure for inflation. Neither study developed a social welfare function to identify the optimal trade-off.
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suggested that such a nonlinear reaction function could be optimal if the Phillips curve were
flat near full output. Alternatively, with a hierarchical mandate, a central bank might be
authorized to pursue output and employment objectives only if inflation remained in the
range (see Stern and Miller, 2004, and Faust and Henderson, 2004). If the range were
breached, inflation control would take precedence.
Finally, an inflation range may also be used, explicitly or implicitly, as an
accountability device. The range may signify a "safe harbor" within which the central bank
would be excused for small deviations from the midpoint goal (Goodfriend, 2005, Lacker,
2005). Mishkin and Westelius (2005) formalize this idea in a model with a fixed penalty on
the central bank for every period that a range is breached. They advocate such a disciplinary
structure as a means of countering political pressures that would over-emphasize
employment objectives. Before evaluating the accountability role of an inflation range, some
theoretical results on optimal accountability standards are reviewed next.
IV. An Optimal Unique Accountability Standard?
Theoretical Considerations
Micro-founded macroeconomic studies have shown that maximizing the welfare of a
representative agent implies a unique targeting criterion for a central bank, the specification
of which depends on the model. These criteria involve relationships among the central
bank's objectives rather than reaction functions for the policy instrument. In general, as
pointed out by Woodford (2004) and references therein, "the target criterion should involve
more than inflation" and, in particular, central banks should "commit themselves to the
pursuit of explicit target criteria that involve real variables as well as inflation." The optimal
target criterion typically involves weighted averages of discounted forecast values for
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inflation and output. Even aside from the complications associated with different
specifications across economic models, the implications of these targeting criteria for the
setting of the policy instrument are complex and controversial. It would be a challenge to
communicate them to the public.
In the face of such challenges, some researchers have assumed that a central bank will
be explicitly accountable only for a single measure of inflation; they then investigate the
theoretical case for determining the optimal measure. For instance, Aoki (2001) explored the
issue of optimal price indexes in a two-sector model. He found that a central bank should
target prices only in the sticky-price sector when prices in the other sector are perfectly
flexible. The idea is that real economic distortions are caused by the deviation of prices from
long-run values, which occurs only in the sticky price sector. Mankiw and Reis (2003)
showed that the optimal weight on the flex-price sector need not be zero if there are sector-
specific markup shocks, in addition to the productivity shocks assumed by Aoki, and if the
sectors also differ in the variance of the shocks, expenditure shares, or responsiveness to the
business cycle. A sticky-price model by Huang and Liu (2005) indicates that policy should
respond to producer prices as well as consumer prices in order to reduce allocative distortions
in the intermediate goods sector. Erceg et al (2000) and Levin et al (2005) find that a central
bank should also place some weight on stabilizing wage inflation to avoid distortions in
labor/leisure choices that could propagate widely in the economy.
Appropriate subsector weights could also depend on differences in the costs of
adjustment to inflation. For instance, consumers may have more costs of compiling accurate
information about inflation developments than firms, so the costs of inflation may be higher
in the consumer sector. Institutionalized indexing arrangements, such as the use of the CPI
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to index Treasury inflation-protected securities and social security retirement benefits, reduce
the cost to insured agents of adjusting to that measure of inflation, suggesting a lower weight,
but may also increase the visibility of the measure and the concern of those who are not
protected, arguing for a higher weight.
Differences in measurement uncertainty could also affect the choice of a price index.
Indeed, some have even argued against announcing an explicit inflation goal partly because
of "conceptual uncertainties and measurement problems" in the indexes (Greenspan, 2004).
Appendix 1 explores one aspect of this issue: the effect of transitory measurement
uncertainties, differing by economic sector, on the choice of an optimal price index in a
Mankiw/Reis type of model. The analysis indicates that the presence of measurement
uncertainty of this nature does not disqualify a sector from an optimal price index, but a
sector's weight in the optimal index depends inversely on the extent of its measurement
uncertainty. In addition, as a caveat to Aoki (2001), the optimal price index entails a positive
weight on a flex-price sector if there is any measurement uncertainty in sticky-price sectors.
This analysis suggests that establishing an inflation target based on a unique official measure
may be suboptimal if that indicator is subject to measurement uncertainties.
This brief review indicates that, just as there is no clear consensus welfare function,
macroeconomic model, or targeting criterion for monetary policy, there is also no theoretical
consensus on specification of an optimal price index. In these circumstances, the typical
practice has been to set aside the search for an optimal index and instead announce a goal
based on a well-known inflation measure. A commonly used indicator is thought likely to
better achieve transparency, credibility, and accountability objectives than a more obscure,
specially constructed measure based on debatable claims to optimality. Some observers have
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gone further to suggest that, in practice, the choice of particular index may not be that
important (see, e.g., Meyer, 2004). This issue is addressed next.
If You've Seen One Price Index, Have You Seen Them All?
Previous studies have documented differences among well-known price indexes in
scope and coverage, subsector weights, estimation procedures, and persistent biases (see,
e.g., Clark, 1999, and Lebow and Rudd, 2003). Despite such differences, however, are the
behaviors of major inflation measures similar enough that stabilizing one of them would
effectively stabilize them all? In particular, suppose the Federal Reserve held inflation as
measured by the core PCE index perfectly constant at some low value.6 How much volatility
would then likely occur in other key inflation measures?
An answer to this question is suggested by the standard deviations of differences in
inflation rates shown in Table 3. Inflation is measured quarterly but based on alternative
averaging periods of one quarter, four quarters, and twenty quarters. The analysis uses the
current definitions of price indexes consistently over time on the assumption that a central
bank would explain and make appropriate adjustments for methodological breaks in series.
Results are given for the period since 1964 and for the two decades of greater inflation
stability since 1983. They suggest that, if core PCE inflation were held perfectly constant,
quarterly inflation as measured by the core CPI index would typically vary from its mean by
close to a percentage point.7 Five-year average core CPI inflation would typically vary from
its mean by one-fourth to one-third of a percentage point. Another way of interpreting this
result is as an indication of how much core PCE inflation would vary if the Fed instead
6 Since June 2004, the Federal Reserve has used the core PCE measure in reporting semi-annual forecasts to Congress. 7 The actual standard deviation of quarterly core CPI inflation has been 2.3 percentage points since 1964 and 1.2 percentage points since 1983.
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stabilized core CPI inflation. Headline inflation measures and GDP chain-weight inflation
(except at the quarterly frequency) would be more volatile.8 Of course, these results are only
suggestive, and they abstract from behavioral responses that could potentially lower volatility
in alternative inflation measures after stabilization of one of the indicators. Nevertheless,
they strengthen the presumption that the choice of inflation indicator does matter; indeed, the
path of a central bank's policy instrument might look quite different depending on which
measure it chooses to stabilize.
Table 3:
Standard Deviation of Difference of Indicated Inflation Rate from Core PCE Inflation
1964:Q2 to 2005:Q3 1983:Q2 to 2005:Q3 Quarters in Averaging → Period
1
4
20
1
4
20
Inflation Measure:
(percentage points)
PCE 1.07 .83 .54 .88 .56 .38
CPI 1.57 1.04 .65 1.53 .91 .62
Core CPI .99 .47 .33 .86 .37 .25
Chain-weight GDP
.98 .77 .70 .82
.63 .51
Is There a Unique Underlying Inflation Process?
But perhaps the well-known inflation indicators all suffer from some idiosyncratic
tendencies that are tangential to what should be the true concern about inflation in the
economy. Perhaps various indexes should be combined in some manner to construct an
indicator of underlying inflation, and the central bank should stabilize that measure.
8 Measures of producer prices (not shown on the table) would be even more volatile.
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This line of thinking presumes that there is a unique underlying inflation process,
which is investigated in Appendix 2, using factor analysis. Empirical tests are conducted to
identify the minimum number of common factors needed to characterize the behavior of
inflation in the United States. The measures include monthly price indexes for total and core
CPI, PCE, and PPI (for finished and intermediate goods), as well as quarterly price indexes
for GDP, nonfarm business output, producers' durable equipment, and imports. In all of the
tests, a single factor was unable to represent the co-movements in these indicators. With
monthly or quarterly data from 1959 on, a single factor was rejected in favor of two factors.
With inclusion of core PPI indexes, available in the period since 1974, additional factors
were needed to account for the co-movements among these inflation indicators. Even when
restricting the analysis to the four core inflation measures or to the four consumer price
measures, a single common factor was insufficient. This analysis suggests that the
inflationary process may be inherently multi-faceted; no improvements in measurement may
ever enable us to derive a unique index that captures even the underlying forces that are
driving inflation. It supports the practice among central banks of making careful evaluation
of a wide variety of inflation indicators, rather than focusing exclusively on any single
measure.
V. Accountability Issues
Inflation Accountability in Principle
In light of the above discussion, would a range for a single inflation measure be a
better accountability structure for a central bank than point-goals for a few reference
measures? Before tackling this question, consider first the role of an accountability structure
when inflation, by one measure, deviates from its goal value. Given lags, that inflation miss
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could have been prevented by a different setting for the monetary policy instrument a year or
so previously. However, if the miss reflected a transitory supply shock, special factor, or
measurement noise that did not affect inflation expectations, the central bank should not have
tried to offset it. Nor should it have countered the miss if it represented an appropriate trade-
off among the central bank's objectives of stabilizing inflation and stabilizing output,
employment, and the financial sector. If instead the miss should have been offset, it would
represent a policy error, at least ex post. Even in this case, though, if the cause was an
unforeseeable shock, an ex ante policy error would not have occurred. But if the inflation
miss was an ex ante error, it presumably could have been avoided with better forecasting by
the central bank or a higher relative weight on inflation in the formulation of policy.
The role of an accountability structure should be to help align a central bank's
incentives to appropriate objectives, which here involves helping to distinguish among the
above cases so that discipline is applied when ex ante policy errors occur and not otherwise.
A poorly constructed accountability framework could misalign incentives in various ways.
For instance, knee-jerk responses of policy instruments to past inflation misses would be
inappropriate, as a change in the current setting of policy would be called for only if an
inflation miss had implications for the inflation forecast. Moreover, an accountability
framework should avoid biasing incentives in favor of stabilizing inflation to the neglect of
other important central bank objectives (Kohn, 2004). In light of these considerations, how
does a single-indicator range compare with multiple inflation indicators as an accountability
structure?
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Accountability with a Range
An inflation range would seem well suited to align incentives to appropriate
objectives if small deviations of inflation from target generally reflected appropriate trade-
offs with other goals or transitory factors that the central bank should have ignored or could
not have foreseen, while large deviations resulting in range breaches were typically
attributable to poor forecasting or an inappropriate weight on inflation. However, the parsing
of inflation misses by size does not always correspond to its parsing by type. Small misses
may be caused by policy errors and may become persistent. Perhaps more importantly, range
breaches are sometimes caused by temporary special factors, generating the use of "escape
clauses" for inflation-targeting central banks and a regular discussion of factors affecting
recent and forecast price developments in inflation reports. The presumption that a range
breach calls for some explanation has itself been challenged by Faust and Henderson (2004).
They claim that, if a range reflects an optimal trade-off between inflation and output stability,
a central bank should be criticized if inflation breaches the range too seldom as well as too
frequently.
Aside from ambiguities regarding the use of a range to identify policy mistakes,
problems arise in devising appropriate penalties for range breaches, and enforcing them. For
instance, the common practice of requiring central banks to offer public explanations when
inflation breaches the range may not represent much of a penalty, as central banks are often
called upon to discuss inflation outcomes and prospects, even when there is no range breach.
On the other hand, if an enforcement device is severe, such as dismissal of a central bank
Governor (as is possible in New Zealand following a range breach), it may almost never be
used.
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Accountability with Point-Values for Several Inflation Indicators
Suppose a central bank announced a goal of low, stable inflation that it would pursue,
given measurement uncertainties, through reference values for a few key inflation measures
used in the formulation of monetary policy. For example, instead of the usual practice of
announcing a goal for headline consumer price inflation, suppose reference values were
announced for total and core consumer prices, and for overall GDP prices. Would
accountability with three reference values of this nature be impaired relative to accountability
under a range for total consumer price inflation?
At first glance, a single inflation measure would seem to have the advantage of
simplicity. Explaining a multiple indicator framework could be more of communication
challenge at the time of announcement of the regime. However, the simplicity of a range
would likely be undermined over time because of the uncertain meaning of the boundaries of
the range. Complexity would also be increased by the need for escape clauses to explain
range breaches.
Over time, transparency and credibility advantages may well accrue to central banks
that announce several inflation reference measures, if those measures are in fact used in
formulating policy. When faced with range breaches caused by special factors, inflation
targeters often point to other, better-behaved inflation indicators in their inflation reports.
Dennis (1997) noted that the hit to credibility from appeals to special factors would be
limited if those factors were identified in advance. Pre-announcing the key inflation
indicators used in formulating policy would also avoid the appearance of making after-the-
fact excuses in such circumstances. Indeed, the use of multiple inflation reference values
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provides a natural framework to facilitate discussion of special factors that beset some
measures but not others.
Multiple indicators and ranges can each be misused, however. On one hand, a range
can be set too wide or escape clauses used too frequently. On the other hand, a central bank
could announce too many official reference measures for inflation and try to avoid
responsibility for any of them. In either case, and especially if the central bank appeared to
be excusing an inflation miss after the fact, credibility could be impaired.
Finally, for a central bank that announces a long-run inflation goal without adopting
other aspects of inflation-targeting, a multiple indicator framework may have a particular
advantage over a single-indicator range. As noted above, an accountability structure risks
making policy subject to backward-looking pressures. Inflation-targeting central banks can
resist such tendencies by drawing attention to forecasts in regular inflation reports and even
making the forecast an intermediate target for policy (Svensson, 1997). However, a central
bank with an inflation goal but without regular inflation reports and forecasts could find itself
subject to greater pressures to respond to recent inflation data, especially if a unique inflation
measure was used. The "discipline" of an over-simplified accountability framework might
then ironically be partly responsible for policy errors.
Experience with Monetary Aggregates
Multiple reference values for inflation might call to mind previous experiences
involving targets for multiple monetary aggregates. Because of the instability of money
demand, monetary aggregates proved unsatisfactory as intermediate targets for many central
banks. Inflation benchmarks represent fundamental objectives for monetary policy, however,
rather than intermediate targets, and for that reason inflation measures could never be
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discarded as an entire class as has often been the case with monetary aggregates.
Nevertheless, individual price indexes are subject to measurement errors and may fall in or
out of favor over time. Thus, some lessons from the experience with monetary aggregates
may apply.
In the case of the Federal Reserve, three key experiences from the monetary targeting
era seem relevant. First, announcing too many official measures may undermine the
credibility of a targeting framework. This may have been the case in the 1970s, when the
Federal Reserve published alternative measures of the monetary base and up to five broader
monetary aggregates at one time (though official targets were only set for up to four
measures). Secondly, frequent introduction of new official measures is also likely to impair
the credibility of a targeting framework, as may have been the case for monetary targeting in
the U.S. in the early 1980s. Thirdly, on the positive side, having more than one official
measure did prove useful to the Federal Reserve in at least one instance: When deregulation
of deposit interest rates undermined the indicator properties of the favored M1 aggregate in
the early 1980s, the presence of previously announced targets for M2 may have helped
facilitate a transition that preserved, at least for a while, the monetary targeting framework.
VI. Conclusion
Central banks with inflation goals have generally used a single measure of inflation as
their official target. A unique reference measure has been seen as advantageous, relative to a
multiple-indicator approach, because of its simplicity. However, unique-indicator regimes
have not been able to maintain that simplicity in practice. Most such regimes employ a
range, rather than a point-value, for their inflation goal. The boundaries of the ranges could
reflect a wide variety of meanings, including those related to a diffuse goal, expected
21
volatility in inflation, alternative policy reaction functions, and accountability structures.
However, inflation-targeting central banks have not typically clarified the meaning of their
inflation ranges, or what should be expected following a range breach. Often, escape clauses
are used to explain that range breaches can be ignored because of special factors. These
departures from simplicity generally seem to be concessions to the inherent complexities of
monetary policy rather than pervasive failures to adhere to an appropriate standard.
More importantly, perhaps, a unique inflation indicator seems an over-
simplification of the way central banks actually go about formulating monetary policy.
Indeed, because of the idiosyncratic effects of special factors across inflation indicators,
careful inspection of multiple indicators seems likely to deliver a better understanding of
underlying inflationary developments. In these circumstances, a case can be made for central
banks to announce that their goal of low, stable inflation will be achieved through the use of
point-values for a few key reference measures of inflation that are important in the
formulation of monetary policy. This approach would not lend itself to expectations of a
mechanical policy response to inflation data, but single-indicator inflation targeters have also
found it advisable to retain elements of discretion, or "flexibility," in implementing their
policy frameworks.
The paper found support for a multiple-indicator approach in two types of analyses.
First, in a theoretical model with sticky and flexible price sectors, optimal monetary policy
needed to consider inflation in only one price measure (that for the sticky price sector), if
there was no measurement uncertainty, as in Aoki (2001). However, when measurement
uncertainty was added to the model, price measures for both the flexible and sticky price
sectors had to be taken into account in formulating policy. Secondly, an empirical
22
investigation of a factor model for U.S. inflation measures suggested that there may be no
unique price measure that can capture underlying inflation processes. Thus, understanding
inflationary developments may inherently require monitoring multiple indicators, as is the
current central bank practice, rather than attempting to devise a unique optimal indicator.
Finally, empirical evidence suggested that stabilizing one inflation indicator was not
equivalent in practice to stabilizing other major inflation measures; indeed, strict targeting of
one measure, to the exclusion of others, could imply quite different paths for policy,
depending on the chosen indicator.
The paper also compared accountability frameworks in regimes with a single-
indicator range to those with multiple inflation indicators. The single-indicator-range
approach seemed preferable only if the official measure rarely gave false signals and if range
breaches were indeed appropriate to avoid. In practice, however, these conditions often do
not hold. Announcing more than one reference measure for inflation would address the
criticism of false precision in inflation goal-setting and likely be more transparent about the
genuine concerns of central bankers in the formulation of policy. Moreover, pre-announcing
alternative inflation reference values, like the pre-announcement of "escape clauses" under
inflation targeting frameworks, may avoid an over-simplified accountability structure and
actually improve the credibility of a central bank's anti-inflationary resolve over time.
Accountability structures can put pressures on the formulation of monetary policy
that are inherently backward-looking and are sometimes misdirected. These pressures would
likely be more intense for a central bank that does not issue regular inflation reports
discussing alternative inflation indicators and providing forecasts as contextual frameworks
for the current setting of policy. For such central banks, a multiple-indicator approach could
23
have a particular advantage over the implementation of an inflation goal through a unique
official inflation measure.
This paper also suggests the desirability of further research on the welfare effects of
maladaptive accountability structures, on the expectations of financial markets and of policy
makers about policy responses at range boundaries for those central banks with inflation
ranges, and on likely economic performance under single- versus multiple-indicator
approaches to inflation targeting.
24
Appendix 1
Optimal Inflation Target with Sector Price Measurement Errors
This appendix depicts a modification of a model developed by Mankiw and Reis
(2003) to allow for measurement error in the sectoral prices observed by the central bank.
Mankiw and Reis show microfoundations for a model whose reduced form version involves
the following price setting behavior by the private sector:
( )
*
* *
1 1
(1 )
1
k k k
k k k k k
K K
k k kk k
P P x
P P E P
P P where
α ε
λ λ
θ θ= =
= + +
= + −
= =∑ ∑
The first equation gives the equilibrium price for sector k as a function of aggregate prices,
P, the output gap, x, and a sector productivity and markup shock, ε. The second equation
reflects sluggish price setting, where some firms respond only to expected values of
equilibrium prices, rather than fully updated values. The third equation gives the aggregate
price measure based on expenditure weights, 2. The model is closed by adding a central
bank that chooses sector weights, w, to form an aggregate price index that it holds constant
while also trying to minimize the variance of the output gap. The central bank’s problem is:
1 1( )( ) . . 0 1.min
k
K K
k k kk kw
Var x s t w P and w= =
= =∑ ∑
In a two-sector implementation of the model, Mankiw and Reis find that a sector with
more sluggish prices should have a larger weight in the central bank’s price index (as long as
the weight is less than unity). They caveat Aoki (2001) by finding that sectors with fully
flexible prices may get a nonzero weight in an optimal index because of sectoral differences
25
in expenditure shares, shock variances, and responsiveness to the business cycle. In
particular, they show that a sector should get a larger weight if it is more responsive to the
business cycle (larger ") or if its productivity and markups are less volatile (smaller Var(ε)).
The Mankiw/Reis model is now modified by assuming that the central bank observes
sector prices with transitory errors uncorrelated across sectors. Private sector agents are not
subject to significant measurement error because of special knowledge of their own and
closely related sectors and because aggregate measurement error is damped by convergence
to the mean value of zero. The central bank's nominal anchor is then given by:
( )1
0K
k k kk
w P μ=
+ =∑ ,
where kμ is an i.i.d. measurement error in sector k. As in Mankiw and Reis, the distributions
of shock variables are known. Using the constraint equations, the output gap can be
expressed as a function of the true sector shocks and the central bank’s measurement errors,
where each variable is expressed as a deviation from its expected value. For a model with
two sectors, A and B:
[ ( )] [1 ( )] [ 1 (1 )][ ( 1) ]( ) ( )( )
A B A A A A A A A A B B A A B A B A A A
A B A A A B B A B A A A B
w w w w w wx
w wλ θ λ ε λ θ λ ε λ θ λ θ μ μ
α λ α λ α λ λ λ θ α α+ − + − − − + − + − − −
= −+ − + − −
.
Taking the variance of x under the assumption of zero covariance among the shocks, the first
order condition for the weight in sector A is:
[ ( )]
(1 ) (1 ) ( )
1 ( ) (1 )( )
B B B B BA A A A AA
BB B B B B BA A A A A A A
A
AB B BA A A A
B
V V V RVwV V QV RV
where Q and R Q
με ε ε
μ με ε
λ α θ λ α ααα λ λ α λ λ θ α αλ
αλ θ λ λ θ α αλ
⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦
⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦
− + +=
− + − + + − +
= − + − = + − −
26
and ijV = Var(ij). The signs of the comparative statics depend in a complex way on the shock
variances and other parameters. However, if we focus on the issues of measurement error
and speed of price adjustment, with other parameters equal across sectors, the optimal weight
is:
(1 )11 ( ) 02(1 ) (1 )
B BAB
BA A
B B BA A ABA
SV Vw where SS SV V V
με
μ με
λ λ λ λ λλ λ λ λ λ λ⎡ ⎤⎣ ⎦
− += = − + >
− + − + +
In this case, it is readily seen that 0 < wA < 1. Increased uncertainty about a sector price
measure implies a smaller weight for the sector in the optimal price index:
2
(1 )0
( 2 )
B BAA B
AAB B BA A A
BA
SV Vw SV S SV V V
με
μμ με
λ λ λλ
λ λ λ λ λ λ⎡ ⎤⎢ ⎥⎢ ⎥⎣ ⎦
− +∂
= − <∂
+ − + +
.
Interestingly, even if there is no measurement uncertainty in other sectors, 0BVμ
= , the
optimal price index does not exclude a sector that is subject to measurement error, but rather
gives it a lower weight depending on the degree of measurement uncertainty.
If prices are perfectly flexible in sector B (λB = 1) but sluggish in sector A, the
optimal weight in sector A is:
12
2B
AA
BA
V VwVV V
με
μμε
λ
≤+
=+ +
.
If there is no measurement uncertainty, 1Aw = , as in Aoki (2001). However, in the presence
of measurement uncertainty regarding prices in the sluggish price sector ( 0AV μ > ), that sector
should not get all the weight in an optimal inflation index.
27
Appendix 2
Factor Model of U.S. Inflation Measures
This appendix reports on tests of the number of factors needed to encompass major
U.S. inflation measures, using the matrix rank test of Cragg and Donald (1997), as
implemented by Swanson (see Gurkaynak, Sack, and Swanson, 2005). If X is a matrix with
n columns, each a time series of a different inflation measure, a factor model for X takes the
form:
X = F·L + ε,
where F is a matrix with m columns, each representing a factor, with m < n, while L is an
m-by-n matrix of factor loadings, and ε is a matrix of white noise errors. Under the null
hypothesis that X can be represented by m common factors, rather than M > m, the minimum
normalized distance between Cov(X) and the model covariance of L'L + Eε has a P2
distribution with ( 1) ( 1)2
n n m m nm− + −− degrees of freedom.
The tests are run on monthly and quarterly data. Monthly series include the total and
core indexes for current methods consumer prices, personal consumption expenditure prices,
and producers' prices for finished goods and intermediate materials. For the quarterly series,
chain-weight price indexes for GDP, nonfarm business output, producers' durable equipment,
and imports are included. A sample period from 1959 through September 2005 is used, as
well as a second period beginning in 1974, which allows inclusion of the core PPI measures.9
The test results are given in Table 4. A p-value greater than 5 percent indicates that
the null hypothesis cannot be rejected, and thus the indicated number of factors can represent
9 Augmented Dickey-Fuller tests rejected a unit root in each of these inflation series over the indicated period.
28
the common movements of the variables. As shown in the table, the tests indicate that the
co-movements among these inflation measures cannot be represented by a single factor. For
monthly data and for quarterly data beginning in 1959, two factors appear to be sufficient.
Additional factors are needed to explain common movements since 1974 in data sets that
include core PPI series.
Table 4 also reports on the "communalities," or proportion of the variance of a
variable explained by the common factors. While loadings on the factors (not shown) may
vary depending on the particular "rotation" chosen for the model, the proportion of the
variance of each price series that is explained by the factors does not change with alternative
rotations. The communalities therefore may be a more useful guide to interpreting the
factors.
The first column of Table 4 indicates that a two-factor monthly model does a good
job of accounting for movements in total and core PCE prices and the total CPI series since
1959, but it explains only 50 to 60 percent of the variance of the core CPI and PPI measures.
The four factors needed to represent co-movements in monthly data since 1974 explain a
high proportion of the variance of most series, though total and core measures of the PPI for
finished goods are less well explained. Separate tests (not shown) indicated rejection at the
one percent level of the null hypothesis that one factor could represent co-movements in the
four monthly core price measures since 1974 or in the four consumer price measures since
1959.
With the smoothing of data in quarterly series, two factors explain large fractions of
the variance of most individual series since 1959, with prices for intermediate goods,
producers' durable equipment, and imports somewhat less well represented. With the three
29
factors called for in quarterly data since 1973, three-fourths or more of the variance of each
price series was explained by common factors. A third factor called for in the period since
1974 considerably boosted the explanatory power for intermediate goods prices.
Table 4
1959:2– 2005:9
1974:2– 2005:9
1959:Q2– 2005:Q3
1974:Q2– 2005:Q3
Monthly Monthly Quarterly Quarterly
Factors 2 4 2 3
p-value on null of # of factors .240 .057 .135 .100
p-value on null of 1 less factor .004 .007 .007 .000
INFLATION MEASURES: Communalities:
CPI (current methods) 0.818 0.959 0.915 0.914
Core CPI (current methods) 0.514 0.901 0.823 0.840
PCE 0.954 0.999 0.985 1.000
Core PCE 1.000 0.971 0.971 0.962
PPI (finished goods) 0.625 0.683 0.851 0.829
Core PPI (finished goods) 0.579 0.885
PPI (intermediate goods) 0.554 0.966 0.756 0.999
Core PPI (intermediate goods) 0.804 0.911
GDP 0.926 0.948
Non-Farm Business Sector 0.885 0.907
Producers Durable Equipment 0.683 0.798
Imports 0.719 0.739
30
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